Answer:
Number of units possible in S are 4.
Explanation:
Given <em>S</em> is a set of complex number of the form  where <em>a</em> and <em>b</em> are integers.
 where <em>a</em> and <em>b</em> are integers.
  is a unit if
 is a unit if  exists such that
 exists such that  .
.
To find:
Number of units possible = ?
Solution:
Given that:

Taking modulus both sides:

Using the property that modulus of product of two complex numbers is equal to their individual modulus multiplied.
i.e.

So, 
 ......... (1)
......... (1)
Let 
Then modulus of z is   
Given that a and b are <em>integers</em>, so the equation (1) can be true only when  (Reciprocal of 1 is 1). Modulus can be equal only when one of the following is satisfied:
 (Reciprocal of 1 is 1). Modulus can be equal only when one of the following is satisfied:
(a = 1, b = 0) ,  (a = -1, b = 0), (a = 0, b = 1) OR (a = 0, b = -1)
So, the possible complex numbers can be:

Hence, number of units possible in S are 4.